1. Field of the Invention
The invention relates to the field of metrology, and in particular to computationally efficient optical metrology systems.
2. Related Art
Optical metrology tools (such as ellipsometry tools or reflectometry tools) determine the attributes of thin films in integrated circuits (ICs) by reflecting a probe beam of light off of the thin films. Data measurements from the reflected beam are collected and compared to an optical model of the thin films and any interfacing structures to generate values for the thin film attribute(s) of interest.
Typically, optical metrology is performed on thin films formed on predetermined target regions of a wafer. Those target regions have historically included thin films formed on uniform (monolithic) base layers. However, as device geometries decrease and IC yield and performance requirements become more sensitive to process defects, monolithic targets (i.e., targets located over monolithic base layers) may not be sufficiently representative of the actual thin film characteristics in the active regions of the IC.
Therefore, modern ICs sometimes incorporate “patterned targets”, i.e., targets located over patterned (non-monolithic) base layers. Typically, a patterned base layer is a grating base layer that can include periodic structures (e.g., lines), which can be formed from metal, silicon, or any other material used in an IC. A patterned base layer allows a metrology operation to be performed on a thin film that more closely resembles the physical, chemical, and mechanical properties of thin film portions in the active device area of the wafer.
Furthermore, as device geometries become smaller, the large planar areas of metal (20-30 um square, which is large compared to transistors) in the base layers of conventional monolithic targets can become problematic. Specifically, such large planar areas of metal can be difficult to accurately produce. For example, chemical-mechanical polishing (CMP) can lead to unacceptable “dishing” as the soft metal (relative to semiconductor and oxide materials) deforms under the CMP slurry load. This dishing can significantly affect the accuracy of any optical metrology techniques used in the region. The softer the metal, the more this problem is amplified, and the more measurement accuracy is degraded. Since a large proportion of a patterned base layer is formed from semiconductor materials (i.e., the metal lines are typically formed in an oxide layer), it is less susceptible to dishing.
Therefore, the use of grating targets can beneficially enhance the quality of optical metrology. Conventional methods for performing optical metrology on grating targets typically involve the same methodology used for metrology on monolithic targets. Specifically, a theoretical model (i.e., a set of equations based upon fundamental optical principles) is created for the grating target. The theoretical model is then used to determine values for the thin film “attribute of interest” (AOI, the thin film attribute for which an output value is desired). This process is described in greater detail with respect to FIGS. 1A-1D.
In FIG. 1A, a theoretical model C(TH) is generated for the test sample. This model can be created by, for example, solving the fundamental Fresnel equations that define the behavior of the probe beam at the test sample. Then, in FIG. 1B, measurement data D(MEAS) for the test sample is collected (often across a range of wavelengths or across a range of incident angles for ellipsometry or reflectometry). Measurement data D(MEAS) can be any ellipsometry measurement parameter, such as α, β, Ψ, or Δ, or any reflectometry measurement parameter, such as reflectivity ().
Next, in FIG. 1C, theoretical model C(TH) is regressed along the AOIs until the difference (error) between the curves for theoretical model C(TH) and measurement data D(MEAS) is below some threshold limit. For example, if thickness is the AOI being determined by the metrology process, appropriate values would be assigned to the other thin film attributes in the theoretical model (e.g., index of refraction, extinction coefficient, material composition), and the thickness value would be varied until the regressed data (curve C(RE)) matched the measured data (curve D(MEAS)), as shown in FIG. 1D. The thickness value at this point could then be output as the thickness of the thin film layer.
This sequence of operations depicted in FIGS. 1A-1D is summarized in the flow diagram of FIG. 1E. Thus, in a “DEFINE FUNDAMENTAL EQUATIONS” step 110, a set of equations that define the behavior of the probe beam at the test sample (e.g., Fresnel equations) are specified. Then, in a “GENERATE THEORETICAL MODEL” step 120, the fundamental equations defined in step 110 are solved to create a theoretical model for the test sample. Steps 110 and 120 therefore correspond to FIG. 1A.
Next, in a “COLLECT MEASUREMENT DATA” step 130, the reflected probe beam data is gathered, as shown in FIG. 1B. The theoretical model is then regressed along the AOI(s) to match the measured data in a “REGRESS MODEL EQUATIONS” step 140. Finally, in an “OUTPUT AOI VALUE(S)” step 150, a value(s) for the AOI(s) of the thin film layer is derived from the regressed model equations.
In this manner, conventional optical metrology systems are able to calculate values for thin film attributes by using a rigorous model of the thin film stack (i.e., the thin film and any underlying layers). Unfortunately, the computational power required to generate the theoretical optical model for a grating-based thin film stack (i.e., a thin film(s) formed over a grating) can be excessive, due to the sheer complexity of the equations that describe the optical behavior of such structures.
For example, an ellipsometry tool measures the ellipsometric angles ψ and Δ, where tan(ψ) is the relative amplitude ratio of the incident and reflected probe beams, while Δ is the relative phase shift between the incident and reflected probe beams. Ellipsometric angles ψ and Δ are related to the complex ratio of the Fresnel reflection coefficients Rp and Rs for light polarized parallel (p) and perpendicular (s) to the plane of incidence by the following equation:tan(ψ)eiΔ=Rp/Rs  [1]where Rp and Rs are the complex Fresnel reflection coefficients at the surface of the film stack for light polarized parallel and perpendicular, respectively, to the plane of incidence.
Fresnel reflection coefficients Rp and Rs are complex functions of the wavelength(s) and angle(s) of incidence of the probe beam, and also of the optical constants (e.g., index of refraction, extinction coefficient) of the materials in the film stack. Specific functions for Fresnel reflection coefficients Rp and Rs can be defined as sets of model equations that are associated with the individual layers making up the film stack.
For example, the reflectivity at the bottom of a layer (just above the top of the layer below) can be expressed as a function of the interface Fresnel reflectance and the effective reflectivity at the top of the layer immediately below the layer of interest, as indicated by the following equation:RB(j)=(RF(j)+RT(j−1)/(1+RF(j)*RT(j−1))  [2]where RB(j) is the reflectance at the bottom of layer j (“lower reflectance”), RF(j) is the interface Fresnel reflectance between layer j and layer j−1 (i.e., the layer immediately below layer j), and RT(j−1) is the reflectance at the top of layer j−1 (“upper reflectance”).
Upper reflectance RT(j−1) can be given by the following:RT(j−1)=RB(j−1) exp(−4πi(n(j−1)d(j−1)cos(θ(j−1))/λ))  [3]where RB(j−1) is the lower reflectance of layer j−1, n(j−1) is the index of refraction of layer j−1, d(j−1) is the thickness of layer j−1, and θ(j−1) is the angle of incidence of the probe beam as it enters layer j−1.
Index of refraction ny can be represented by the Cauchy equation:n(j−1)=A(j−1)+B(j−1)/λ2+C(j−1)/λ4  [4]where A(j−1), B(j−1), and C(j−1) are Cauchy coefficients for index of refraction that depend on the material properties of layer j−1 and the wavelength λ of the probe beam. Note that various other equations can be used to define index of refraction.
Note further that depending on the properties of the various material layers, index of refraction n(j−1) may need to be replaced with the more accurate “complex index of refraction” N(j−1), which has both real and imaginary portions, as indicated below:N(j−1)=n(j−1)+ik(j−1)  [5]where k(j−1) is the extinction coefficient for the appropriate material layer given by:k(j−1)=D(j−1)+E(j−1)/λ2+F(j−1)/λ4  [6]where D(j−1), E(j−1), and F(j−1) are Cauchy coefficients for extinction that depend on the material properties of layer j−1 and the wavelength λ of the probe beam.
Meanwhile, interface Fresnel reflectance RF(j) is given by the following:RF(j)=(p(j)−p(j−1))/(p(j)+p(j−1))  [7]where p(j) and p(j−1) represent dispersion factors for layers j and j−1, respectively. For light polarized in the parallel direction (i.e., the direction parallel to the plane of incidence), dispersion factor p(j) is given by the following:p(j)=n(j)cos(θ(j))  [8]where n(j) is the index of refraction of layer j, and θ(j) is the angle of incidence of the probe beam as it enters layer j. For light polarized in the in the perpendicular direction (i.e., perpendicular to the plane of incidence), dispersion factor p(j) is given by the following:p(j)=cos(θ(j))/n(j)  [9]Dispersion factor p(j−1) for is calculated in a similar manner for the two light polarizations.
Equation 2 can be used to define a lower reflectance equation for each layer of the film stack. This results in a first set of reflectance equations for light polarized in the parallel direction (based on Equations 2 through 8) and a second set of reflectance equations for light polarized in the perpendicular direction (based on Equations 2 through 7 and 9). Within the first and second sets of reflectance equations, if the ambient environment is defined as the topmost “layer” in the film stack, the lower reflectance equation for that ambient layer is equivalent to Fresnel reflection coefficients Rp and Rs, respectively. Therefore, by solving the first and second recursive sets of reflectance equations, the model equations for the film stack can be fully defined.
Note that because the lower reflectance of a given layer is a function of the upper reflectance of the layer below that given layer, each of the two sets of reflectance equations is a recursive set. Note further that the reflectance at the substrate is defined to be zero, which provides a starting point from which both sets of recursive reflectance equations can be solved.
Clearly, the more layers present in the film stack, the more complex the model equation determination becomes. Even so, processing the model equations for a large multi-layer film stack formed on a monolithic base layer can still be performed using reasonable computational power.
However, the incorporation of a patterned base layer under the thin film(s) complicates the Fresnel equations by several orders of magnitude, since the grating structure introduces a large number of additional material interfaces.
Each of these new interfaces has its own reflection and refraction effects, and requires additional description (equations). A sample formal derivation of Maxwell's equations for a thin film on a patterned base layer is described in “Formulation for Stable and Efficient Implementation of the Rigorous Coupled-Wave Analysis of Binary Gratings”, M. G. Moharam et al., J. Opt. Soc. Am. A, Vol. 12, pp. 1068-1076 (1995), herein incorporated by reference.
Solving the immensely larger set of equations for a grating target is significantly more difficult than solving the equations for a monolithic target and can require on the order of ten thousand times the computing resources required to solve the monolithic target equations. Therefore, metrology systems that use conventional processing techniques to analyze grating targets can be expensive, cumbersome, and slow, due to the sheer volume of computing resources required (both hardware and software resources).
Various approaches have been considered in an effort to reduce some of the computational load placed on metrology systems when analyzing grating targets. For example, the patterned base layer can be treated as a solid layer, thereby simplifying the model equations. The model equations could also be simplified by ignoring phase information and only using reflected intensity data in the calculations. However, in either case, the approximations can result in unacceptable inaccuracy in the final measurement values.
Accordingly, it is desirable to provide a computationally efficient method and system for accurately measuring thin films formed on patterned base layers.